A positron CT device, i.e., a PET (Positron Emission Tomography) device reconstructs an image of a subject only upon detection of positrons, i.e., gamma rays generated in annihilation of the positrons and detection of the gamma rays simultaneously with a detector (that is, only upon coincidence).
The PET device of this type doses a subject with a radiopharmaceutical, and thereafter determines accumulation of the drug in a target tissue temporally. As a result, various body functions may be determined quantitatively. Consequently, an image that the PET device obtains has functional information.
Description will be given in detail to a human body as one example of a subject. Positron radioisotope, such as 15O, 18F, and 11C, is injected inside the subject body to detect gamma rays to be generated upon binding of positrons emitted from the radioisotope to electrons. The gamma rays are detected with a row of detectors that are composed of numerous gamma-ray detectors arranged in a ring shape so as to surround a body axis as a longitudinal axis of the subject. Thereafter, a computer calculates in the same process as the conventional X-ray computed tomography to specify gamma rays in a plane, thereby creating an image of the subject.
The following process is adopted in image reconstruction. See, for example, Non-patent Literatures 1 and 2. Let a pixel formed in three-dimensional voxels within an FOV (Field of View) be denoted by vj (j=0, 1, . . . , J−1), and i-th LOR (Line Of Response) by Li (i=0, 1, . . . , I−1.) Here, LOR is a virtual line connecting two detectors that perform coincidence. Where the pixel is composed of three-dimensional voxels, LOR corresponds to a tube region made by connecting two detectors that detects two gamma-ray photons generated from each voxel and emitted in the opposite directions.
In reconstruction of PET images, i.e. a probability that gamma-ray photons emission from voxel vj is detected in the LOR (Li), has an important function. The aij is referred to as a “system matrix.” As for formulization of image reconstruction, see Non-patent Literatures 1 and 2.
It is difficult to calculate aij precisely. One process is used to provide sampling points inside the detectors on both ends of each Li and to make approximation of the sum of the probability aij(s) where the gamma-ray photons generated from vj are detected in a minute region of the detectors with the following Equation (4). See, for example, Non-patent Literature 3.
[Non-Patent Literature 1]
Nakamura T, Kudo H: Derivation and implementation of ordered-subsets algorithms for list-mode PET data, IEEE Nuclear Science Symposium Conference Record: 1950-1954, 2005
[Non-Patent Literature 2]
Tanaka E, Kudo H: Subset-dependent relaxation in block-iterative algorithms for image reconstruction in emission tomography. In: Phys Med Biol 48, 1405-1422, 2003
[Non-Patent Literature 3]
Hisashi Takahashi, Taiga Tamaya, Tetsuya Kobayashi et al.: Imaging system models for small bore DOI-PET scanners, JAMIT Annual Meeting 2006 proceedings OP10-7
[Non-Patent Literature 4]
H. Tonami, K. Kitamura, M. Satoh, T. Tsuda, and Y. Kumazawa, “Sophisticated 32×32×4-Layer DOI Detector for High Resolution PEM Scanner,” IEEE Medical Imaging Conference Record, pp. 3803-3807, 2007